Statistics.Sample:$swelfordMean from math-functions-0.1.5.2

Percentage Accurate: 100.0% → 100.0%

Time: 6.4s

Alternatives: 7

Speedup: 1.0×

• 20.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{z} \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + \frac{y - x}{z} \]
4. Add Preprocessing

Alternative 2: 61.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-285}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-268}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -2.2e+26)
     x
     (if (<= z -2.8e-74)
       (/ y z)
       (if (<= z -1.05e-285)
         t_0
         (if (<= z 9.2e-268)
           (/ y z)
           (if (<= z 2e-133)
             t_0
             (if (<= z 2.6e-78) (/ y z) (if (<= z 1.0) t_0 x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -2.2e+26) {
		tmp = x;
	} else if (z <= -2.8e-74) {
		tmp = y / z;
	} else if (z <= -1.05e-285) {
		tmp = t_0;
	} else if (z <= 9.2e-268) {
		tmp = y / z;
	} else if (z <= 2e-133) {
		tmp = t_0;
	} else if (z <= 2.6e-78) {
		tmp = y / z;
	} else if (z <= 1.0) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -x / z
    if (z <= (-2.2d+26)) then
        tmp = x
    else if (z <= (-2.8d-74)) then
        tmp = y / z
    else if (z <= (-1.05d-285)) then
        tmp = t_0
    else if (z <= 9.2d-268) then
        tmp = y / z
    else if (z <= 2d-133) then
        tmp = t_0
    else if (z <= 2.6d-78) then
        tmp = y / z
    else if (z <= 1.0d0) then
        tmp = t_0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -2.2e+26) {
		tmp = x;
	} else if (z <= -2.8e-74) {
		tmp = y / z;
	} else if (z <= -1.05e-285) {
		tmp = t_0;
	} else if (z <= 9.2e-268) {
		tmp = y / z;
	} else if (z <= 2e-133) {
		tmp = t_0;
	} else if (z <= 2.6e-78) {
		tmp = y / z;
	} else if (z <= 1.0) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -2.2e+26:
		tmp = x
	elif z <= -2.8e-74:
		tmp = y / z
	elif z <= -1.05e-285:
		tmp = t_0
	elif z <= 9.2e-268:
		tmp = y / z
	elif z <= 2e-133:
		tmp = t_0
	elif z <= 2.6e-78:
		tmp = y / z
	elif z <= 1.0:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -2.2e+26)
		tmp = x;
	elseif (z <= -2.8e-74)
		tmp = Float64(y / z);
	elseif (z <= -1.05e-285)
		tmp = t_0;
	elseif (z <= 9.2e-268)
		tmp = Float64(y / z);
	elseif (z <= 2e-133)
		tmp = t_0;
	elseif (z <= 2.6e-78)
		tmp = Float64(y / z);
	elseif (z <= 1.0)
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x / z;
	tmp = 0.0;
	if (z <= -2.2e+26)
		tmp = x;
	elseif (z <= -2.8e-74)
		tmp = y / z;
	elseif (z <= -1.05e-285)
		tmp = t_0;
	elseif (z <= 9.2e-268)
		tmp = y / z;
	elseif (z <= 2e-133)
		tmp = t_0;
	elseif (z <= 2.6e-78)
		tmp = y / z;
	elseif (z <= 1.0)
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -2.2e+26], x, If[LessEqual[z, -2.8e-74], N[(y / z), $MachinePrecision], If[LessEqual[z, -1.05e-285], t$95$0, If[LessEqual[z, 9.2e-268], N[(y / z), $MachinePrecision], If[LessEqual[z, 2e-133], t$95$0, If[LessEqual[z, 2.6e-78], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.0], t$95$0, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.20000000000000007e26 or 1 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

      2. associate-+r- 100.0%

         \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

      3. remove-double-neg 100.0%

         \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

      4. distribute-frac-neg 100.0%

         \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

      5. unsub-neg 100.0%

         \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

      6. associate--r+ 100.0%

         \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

      8. distribute-frac-neg 100.0%

         \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      9. sub-neg 100.0%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

      10. div-sub 100.0%

          \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 75.4%

      \[\leadsto \color{blue}{x} \]

   if -2.20000000000000007e26 < z < -2.79999999999999988e-74 or -1.04999999999999992e-285 < z < 9.20000000000000042e-268 or 2.0000000000000001e-133 < z < 2.6000000000000001e-78

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 95.3%

         \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

      2. associate-+r- 95.3%

         \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

      3. remove-double-neg 95.3%

         \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

      4. distribute-frac-neg 95.3%

         \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

      5. unsub-neg 95.3%

         \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

      6. associate--r+ 95.3%

         \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

      7. +-commutative 95.3%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

      8. distribute-frac-neg 95.3%

         \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      9. sub-neg 95.3%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

      10. div-sub 100.0%

          \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 70.6%

      \[\leadsto \color{blue}{\frac{y}{z}} \]

   if -2.79999999999999988e-74 < z < -1.04999999999999992e-285 or 9.20000000000000042e-268 < z < 2.0000000000000001e-133 or 2.6000000000000001e-78 < z < 1

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 97.8%

         \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

      2. associate-+r- 97.8%

         \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

      3. remove-double-neg 97.8%

         \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

      4. distribute-frac-neg 97.8%

         \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

      5. unsub-neg 97.8%

         \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

      6. associate--r+ 97.8%

         \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

      7. +-commutative 97.8%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

      8. distribute-frac-neg 97.8%

         \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      9. sub-neg 97.8%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

      10. div-sub 100.0%

          \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 68.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{z}\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 68.7%

         \[\leadsto \color{blue}{x \cdot 1 - x \cdot \frac{1}{z}} \]

      2. *-rgt-identity 68.7%

         \[\leadsto \color{blue}{x} - x \cdot \frac{1}{z} \]

      3. associate-*r/ 68.8%

         \[\leadsto x - \color{blue}{\frac{x \cdot 1}{z}} \]

      4. *-rgt-identity 68.8%

         \[\leadsto x - \frac{\color{blue}{x}}{z} \]

   7. Simplified 68.8%

      \[\leadsto \color{blue}{x - \frac{x}{z}} \]

   8. Taylor expanded in z around 0 67.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 67.2%

         \[\leadsto \color{blue}{-\frac{x}{z}} \]

   10. Simplified 67.2%

       \[\leadsto \color{blue}{-\frac{x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-285}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-268}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-133}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-78}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{z}\\ t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{-75}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-267}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-73}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 0.06:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y z))) (t_1 (/ (- x) z)))
   (if (<= z -4.5e-75)
     t_0
     (if (<= z -2.9e-286)
       t_1
       (if (<= z 1.15e-267)
         (/ y z)
         (if (<= z 3e-132)
           t_1
           (if (<= z 2.45e-73) (/ y z) (if (<= z 0.06) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y / z);
	double t_1 = -x / z;
	double tmp;
	if (z <= -4.5e-75) {
		tmp = t_0;
	} else if (z <= -2.9e-286) {
		tmp = t_1;
	} else if (z <= 1.15e-267) {
		tmp = y / z;
	} else if (z <= 3e-132) {
		tmp = t_1;
	} else if (z <= 2.45e-73) {
		tmp = y / z;
	} else if (z <= 0.06) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + (y / z)
    t_1 = -x / z
    if (z <= (-4.5d-75)) then
        tmp = t_0
    else if (z <= (-2.9d-286)) then
        tmp = t_1
    else if (z <= 1.15d-267) then
        tmp = y / z
    else if (z <= 3d-132) then
        tmp = t_1
    else if (z <= 2.45d-73) then
        tmp = y / z
    else if (z <= 0.06d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y / z);
	double t_1 = -x / z;
	double tmp;
	if (z <= -4.5e-75) {
		tmp = t_0;
	} else if (z <= -2.9e-286) {
		tmp = t_1;
	} else if (z <= 1.15e-267) {
		tmp = y / z;
	} else if (z <= 3e-132) {
		tmp = t_1;
	} else if (z <= 2.45e-73) {
		tmp = y / z;
	} else if (z <= 0.06) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y / z)
	t_1 = -x / z
	tmp = 0
	if z <= -4.5e-75:
		tmp = t_0
	elif z <= -2.9e-286:
		tmp = t_1
	elif z <= 1.15e-267:
		tmp = y / z
	elif z <= 3e-132:
		tmp = t_1
	elif z <= 2.45e-73:
		tmp = y / z
	elif z <= 0.06:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y / z))
	t_1 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -4.5e-75)
		tmp = t_0;
	elseif (z <= -2.9e-286)
		tmp = t_1;
	elseif (z <= 1.15e-267)
		tmp = Float64(y / z);
	elseif (z <= 3e-132)
		tmp = t_1;
	elseif (z <= 2.45e-73)
		tmp = Float64(y / z);
	elseif (z <= 0.06)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y / z);
	t_1 = -x / z;
	tmp = 0.0;
	if (z <= -4.5e-75)
		tmp = t_0;
	elseif (z <= -2.9e-286)
		tmp = t_1;
	elseif (z <= 1.15e-267)
		tmp = y / z;
	elseif (z <= 3e-132)
		tmp = t_1;
	elseif (z <= 2.45e-73)
		tmp = y / z;
	elseif (z <= 0.06)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -4.5e-75], t$95$0, If[LessEqual[z, -2.9e-286], t$95$1, If[LessEqual[z, 1.15e-267], N[(y / z), $MachinePrecision], If[LessEqual[z, 3e-132], t$95$1, If[LessEqual[z, 2.45e-73], N[(y / z), $MachinePrecision], If[LessEqual[z, 0.06], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5000000000000003e-75 or 0.059999999999999998 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

      2. associate-+r- 100.0%

         \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

      3. remove-double-neg 100.0%

         \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

      4. distribute-frac-neg 100.0%

         \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

      5. unsub-neg 100.0%

         \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

      6. associate--r+ 100.0%

         \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

      8. distribute-frac-neg 100.0%

         \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      9. sub-neg 100.0%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

      10. div-sub 100.0%

          \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 95.7%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. neg-mul-1 95.7%

         \[\leadsto x - \color{blue}{\left(-\frac{y}{z}\right)} \]

      2. distribute-neg-frac 95.7%

         \[\leadsto x - \color{blue}{\frac{-y}{z}} \]

   7. Simplified 95.7%

      \[\leadsto x - \color{blue}{\frac{-y}{z}} \]

   8. Taylor expanded in x around 0 95.7%

      \[\leadsto \color{blue}{x + \frac{y}{z}} \]
   9. Step-by-step derivation

      1. +-commutative 95.7%

         \[\leadsto \color{blue}{\frac{y}{z} + x} \]

   10. Simplified 95.7%

       \[\leadsto \color{blue}{\frac{y}{z} + x} \]

   if -4.5000000000000003e-75 < z < -2.8999999999999998e-286 or 1.15000000000000003e-267 < z < 3e-132 or 2.45000000000000014e-73 < z < 0.059999999999999998

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 97.8%

         \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

      2. associate-+r- 97.8%

         \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

      3. remove-double-neg 97.8%

         \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

      4. distribute-frac-neg 97.8%

         \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

      5. unsub-neg 97.8%

         \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

      6. associate--r+ 97.8%

         \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

      7. +-commutative 97.8%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

      8. distribute-frac-neg 97.8%

         \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      9. sub-neg 97.8%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

      10. div-sub 100.0%

          \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 68.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{z}\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 68.7%

         \[\leadsto \color{blue}{x \cdot 1 - x \cdot \frac{1}{z}} \]

      2. *-rgt-identity 68.7%

         \[\leadsto \color{blue}{x} - x \cdot \frac{1}{z} \]

      3. associate-*r/ 68.8%

         \[\leadsto x - \color{blue}{\frac{x \cdot 1}{z}} \]

      4. *-rgt-identity 68.8%

         \[\leadsto x - \frac{\color{blue}{x}}{z} \]

   7. Simplified 68.8%

      \[\leadsto \color{blue}{x - \frac{x}{z}} \]

   8. Taylor expanded in z around 0 67.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} \]
   9. Step-by-step derivation

      1. mul-1-neg 67.2%

         \[\leadsto \color{blue}{-\frac{x}{z}} \]

   10. Simplified 67.2%

       \[\leadsto \color{blue}{-\frac{x}{z}} \]

   if -2.8999999999999998e-286 < z < 1.15000000000000003e-267 or 3e-132 < z < 2.45000000000000014e-73

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 91.3%

         \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

      2. associate-+r- 91.3%

         \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

      3. remove-double-neg 91.3%

         \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

      4. distribute-frac-neg 91.3%

         \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

      5. unsub-neg 91.3%

         \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

      6. associate--r+ 91.3%

         \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

      7. +-commutative 91.3%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

      8. distribute-frac-neg 91.3%

         \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      9. sub-neg 91.3%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

      10. div-sub 100.0%

          \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 74.7%

      \[\leadsto \color{blue}{\frac{y}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-75}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-286}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-267}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-132}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-73}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 0.06:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6400000 \lor \neg \left(x \leq 7 \cdot 10^{-88} \lor \neg \left(x \leq 1.45 \cdot 10^{-71}\right) \land x \leq 1.85 \cdot 10^{-7}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6400000.0)
         (not (or (<= x 7e-88) (and (not (<= x 1.45e-71)) (<= x 1.85e-7)))))
   (- x (/ x z))
   (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6400000.0) || !((x <= 7e-88) || (!(x <= 1.45e-71) && (x <= 1.85e-7)))) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-6400000.0d0)) .or. (.not. (x <= 7d-88) .or. (.not. (x <= 1.45d-71)) .and. (x <= 1.85d-7))) then
        tmp = x - (x / z)
    else
        tmp = x + (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6400000.0) || !((x <= 7e-88) || (!(x <= 1.45e-71) && (x <= 1.85e-7)))) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6400000.0) or not ((x <= 7e-88) or (not (x <= 1.45e-71) and (x <= 1.85e-7))):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6400000.0) || !((x <= 7e-88) || (!(x <= 1.45e-71) && (x <= 1.85e-7))))
		tmp = Float64(x - Float64(x / z));
	else
		tmp = Float64(x + Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6400000.0) || ~(((x <= 7e-88) || (~((x <= 1.45e-71)) && (x <= 1.85e-7)))))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6400000.0], N[Not[Or[LessEqual[x, 7e-88], And[N[Not[LessEqual[x, 1.45e-71]], $MachinePrecision], LessEqual[x, 1.85e-7]]]], $MachinePrecision]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.4e6 or 7.0000000000000002e-88 < x < 1.4499999999999999e-71 or 1.85000000000000002e-7 < x

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 97.2%

         \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

      2. associate-+r- 97.2%

         \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

      3. remove-double-neg 97.2%

         \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

      4. distribute-frac-neg 97.2%

         \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

      5. unsub-neg 97.2%

         \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

      6. associate--r+ 97.2%

         \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

      7. +-commutative 97.2%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

      8. distribute-frac-neg 97.2%

         \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      9. sub-neg 97.2%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

      10. div-sub 100.0%

          \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 92.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{z}\right)} \]
   6. Step-by-step derivation

      1. distribute-lft-out-- 92.6%

         \[\leadsto \color{blue}{x \cdot 1 - x \cdot \frac{1}{z}} \]

      2. *-rgt-identity 92.6%

         \[\leadsto \color{blue}{x} - x \cdot \frac{1}{z} \]

      3. associate-*r/ 92.7%

         \[\leadsto x - \color{blue}{\frac{x \cdot 1}{z}} \]

      4. *-rgt-identity 92.7%

         \[\leadsto x - \frac{\color{blue}{x}}{z} \]

   7. Simplified 92.7%

      \[\leadsto \color{blue}{x - \frac{x}{z}} \]

   if -6.4e6 < x < 7.0000000000000002e-88 or 1.4499999999999999e-71 < x < 1.85000000000000002e-7

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

      2. associate-+r- 100.0%

         \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

      3. remove-double-neg 100.0%

         \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

      4. distribute-frac-neg 100.0%

         \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

      5. unsub-neg 100.0%

         \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

      6. associate--r+ 100.0%

         \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

      8. distribute-frac-neg 100.0%

         \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      9. sub-neg 100.0%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

      10. div-sub 100.0%

          \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 91.4%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. neg-mul-1 91.4%

         \[\leadsto x - \color{blue}{\left(-\frac{y}{z}\right)} \]

      2. distribute-neg-frac 91.4%

         \[\leadsto x - \color{blue}{\frac{-y}{z}} \]

   7. Simplified 91.4%

      \[\leadsto x - \color{blue}{\frac{-y}{z}} \]

   8. Taylor expanded in x around 0 91.4%

      \[\leadsto \color{blue}{x + \frac{y}{z}} \]
   9. Step-by-step derivation

      1. +-commutative 91.4%

         \[\leadsto \color{blue}{\frac{y}{z} + x} \]

   10. Simplified 91.4%

       \[\leadsto \color{blue}{\frac{y}{z} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6400000 \lor \neg \left(x \leq 7 \cdot 10^{-88} \lor \neg \left(x \leq 1.45 \cdot 10^{-71}\right) \land x \leq 1.85 \cdot 10^{-7}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -90 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -90.0) (not (<= z 1.0))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -90.0) || !(z <= 1.0)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-90.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = x + (y / z)
    else
        tmp = (y - x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -90.0) || !(z <= 1.0)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -90.0) or not (z <= 1.0):
		tmp = x + (y / z)
	else:
		tmp = (y - x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -90.0) || !(z <= 1.0))
		tmp = Float64(x + Float64(y / z));
	else
		tmp = Float64(Float64(y - x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -90.0) || ~((z <= 1.0)))
		tmp = x + (y / z);
	else
		tmp = (y - x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -90.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -90 or 1 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

      2. associate-+r- 100.0%

         \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

      3. remove-double-neg 100.0%

         \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

      4. distribute-frac-neg 100.0%

         \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

      5. unsub-neg 100.0%

         \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

      6. associate--r+ 100.0%

         \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

      8. distribute-frac-neg 100.0%

         \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      9. sub-neg 100.0%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

      10. div-sub 100.0%

          \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 98.1%

      \[\leadsto x - \color{blue}{-1 \cdot \frac{y}{z}} \]
   6. Step-by-step derivation

      1. neg-mul-1 98.1%

         \[\leadsto x - \color{blue}{\left(-\frac{y}{z}\right)} \]

      2. distribute-neg-frac 98.1%

         \[\leadsto x - \color{blue}{\frac{-y}{z}} \]

   7. Simplified 98.1%

      \[\leadsto x - \color{blue}{\frac{-y}{z}} \]

   8. Taylor expanded in x around 0 98.1%

      \[\leadsto \color{blue}{x + \frac{y}{z}} \]
   9. Step-by-step derivation

      1. +-commutative 98.1%

         \[\leadsto \color{blue}{\frac{y}{z} + x} \]

   10. Simplified 98.1%

       \[\leadsto \color{blue}{\frac{y}{z} + x} \]

   if -90 < z < 1

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 96.8%

         \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

      2. associate-+r- 96.8%

         \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

      3. remove-double-neg 96.8%

         \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

      4. distribute-frac-neg 96.8%

         \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

      5. unsub-neg 96.8%

         \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

      6. associate--r+ 96.8%

         \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

      7. +-commutative 96.8%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

      8. distribute-frac-neg 96.8%

         \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      9. sub-neg 96.8%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

      10. div-sub 100.0%

          \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 98.7%

      \[\leadsto \color{blue}{\frac{y - x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -90 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+19}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.5e+26) x (if (<= z 9e+19) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.5e+26) {
		tmp = x;
	} else if (z <= 9e+19) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-6.5d+26)) then
        tmp = x
    else if (z <= 9d+19) then
        tmp = y / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.5e+26) {
		tmp = x;
	} else if (z <= 9e+19) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.5e+26:
		tmp = x
	elif z <= 9e+19:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.5e+26)
		tmp = x;
	elseif (z <= 9e+19)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.5e+26)
		tmp = x;
	elseif (z <= 9e+19)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.5e+26], x, If[LessEqual[z, 9e+19], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.50000000000000022e26 or 9e19 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 100.0%

         \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

      2. associate-+r- 100.0%

         \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

      3. remove-double-neg 100.0%

         \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

      4. distribute-frac-neg 100.0%

         \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

      5. unsub-neg 100.0%

         \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

      6. associate--r+ 100.0%

         \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

      7. +-commutative 100.0%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

      8. distribute-frac-neg 100.0%

         \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      9. sub-neg 100.0%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

      10. div-sub 100.0%

          \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 77.3%

      \[\leadsto \color{blue}{x} \]

   if -6.50000000000000022e26 < z < 9e19

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 97.1%

         \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

      2. associate-+r- 97.1%

         \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

      3. remove-double-neg 97.1%

         \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

      4. distribute-frac-neg 97.1%

         \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

      5. unsub-neg 97.1%

         \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

      6. associate--r+ 97.1%

         \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

      7. +-commutative 97.1%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

      8. distribute-frac-neg 97.1%

         \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

      9. sub-neg 97.1%

         \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

      10. div-sub 100.0%

          \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 48.1%

      \[\leadsto \color{blue}{\frac{y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+19}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{z} \]
2. Step-by-step derivation

   1. div-sub 98.4%

      \[\leadsto x + \color{blue}{\left(\frac{y}{z} - \frac{x}{z}\right)} \]

   2. associate-+r- 98.4%

      \[\leadsto \color{blue}{\left(x + \frac{y}{z}\right) - \frac{x}{z}} \]

   3. remove-double-neg 98.4%

      \[\leadsto \left(x + \color{blue}{\left(-\left(-\frac{y}{z}\right)\right)}\right) - \frac{x}{z} \]

   4. distribute-frac-neg 98.4%

      \[\leadsto \left(x + \left(-\color{blue}{\frac{-y}{z}}\right)\right) - \frac{x}{z} \]

   5. unsub-neg 98.4%

      \[\leadsto \color{blue}{\left(x - \frac{-y}{z}\right)} - \frac{x}{z} \]

   6. associate--r+ 98.4%

      \[\leadsto \color{blue}{x - \left(\frac{-y}{z} + \frac{x}{z}\right)} \]

   7. +-commutative 98.4%

      \[\leadsto x - \color{blue}{\left(\frac{x}{z} + \frac{-y}{z}\right)} \]

   8. distribute-frac-neg 98.4%

      \[\leadsto x - \left(\frac{x}{z} + \color{blue}{\left(-\frac{y}{z}\right)}\right) \]

   9. sub-neg 98.4%

      \[\leadsto x - \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} \]

   10. div-sub 100.0%

       \[\leadsto x - \color{blue}{\frac{x - y}{z}} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 38.1%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 38.1%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024018 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))